Good job for your DD!
I did want to touch on the privates thing... Different girls have different advantages. Some girls are natural gymnasts. In a way, that is an advantage over the kid who has to work her butt off for every skill. Some girls have coaches who really prefer them over some of the other girls, another advantage. Some girls have parents who are coaches... definite advantage.
Some girls are naturally strong. Or naturally flexible. And yes, some girls have parents who can afford to pay for privates. Sometimes this is an advantage that those girls have; but sometimes those girls need that one on one to help them get stuff. Maybe they have a hard time learning in an environment where the coach can't take time with them. Maybe the girl has a confidence issue and this helps her.
I admit, my kids have done privates off an on since starting to do team gymnastics. My son way less than my girls because he requests it less. I generally do it when the kid comes up to me and says that they want to do a private for X, Y, Z reasons. Sometimes it is that they need the repetition that they can get in a private that they can't get in a normal practice. Sometimes it is that they need the little nit picking of routines that can be done more easily in a private. But it is always because they want to be there and to help build their confidence. Ultimately... yes, they have the advantage of parents who can afford some privates. Maybe that will be a drop in the bucket to help make up for the genetic disadvantages that DH and I gave them, like flat feet, slow twitch muscles, scoliosis, etc.